Method and system utilizing parameter-less filter for substantially reducing streak and or noise in computer tomography (CT) images

ABSTRACT

Photon starvation causes streaks and noise and seriously impairs the diagnostic value of the CT imaging. To reduce streaks and noise, a new scheme of adaptive Gaussian filtering relies on the diffusion-derived scale-space concept in one embodiment of the current invention. In scale-space view, filtering by Gaussians of different sizes is similar to decompose the data into a sequence of scales. As the scale measure, the variance of the filter linearly relates to the noise standard deviation of a predetermined noise model in the new filtering method. The new filter has only one optional parameter that remains stable once tuned. Although single-pass processing using the new filter generally achieves desired results, iterations are optionally performed.

FIELD OF THE INVENTION

The current invention generally relates to an image processing methodand system for substantially reducing streak and or noise in computertomography images using a predetermined filter.

BACKGROUND OF THE INVENTION

Noise and streaks due to photon starvation can seriously corrupt thequality of X-ray CT images. Although an increased dose of X-ray mayalleviate the problem, it is not clinically acceptable for patientsafety. To achieve diagnostically useful image quality at a safe dosagelevel, prior art attempts have sought for decades a desirable solutionfor substantially reducing noise and streaks. With an elevated awarenessof low doses, the above described research filed has recently gainedgreat importance and received serious attention.

To improve results, prior efforts have utilized adaptive filters in lieuof fixed filters. Some examples of the fixed filters include atriangular filter and a bilateral filter. Similarly, some examples ofthe adaptive filters include an adaptive Gaussian filter and an adaptivetrimmed mean filter. Among the prior art adaptive filters, the filterparameters still need to be adjusted for the same type or set ofprojection data, and the adjustment relies on an empirical and or ad hocoptimal. In another exemplary filter, the variance of a Gaussian filterkernel is the same as the noise variance of the data. Due to the ad hocnature, the above described prior art adaptive filters insufficientlyreduce noise and or streaks.

It remains desired to have an effective filter to maximize the noise andstreak reduction while its filter parameters are not adjusted in acomplex or ad hoc manner.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating one embodiment of the multi-slice X-rayCT apparatus or scanner according to the current invention.

FIG. 2 is a graph illustrating a relationship between the variancepredicted by the noise model (y-axis) and real measured variance(x-axis).

FIG. 3 is a graph illustrating a relationship between the variancepredicted by the noise model (y-axis) and real measured variance(x-axis) in counts range of FIG. 2 and an extended low count range wherethe relationship becomes highly non-linear.

FIG. 4 is a graph illustrating a relationship between the effectivefilter size of the Gauss filter and the count with respect to thedimension N, VarScale and VarPower using a predetermined Gaussianfilter.

FIG. 5 is a graph illustrating a relation between the mean count and theafter-log variance after filtering in an embodiment of the noise and orstreak reduction device using a predetermined filter with a first set ofparameter values according to the current invention.

FIG. 6 is a graph illustrating a relation between the mean count and theafter-log variance after filtering in an embodiment of the noise and orstreak reduction device using a predetermined filter with a second setof parameter values according to the current invention.

FIG. 7 is a graph illustrating a relation between the mean count and theafter-log variance after filtering in an embodiment of the noise and orstreak reduction device using a predetermined filter with a third set ofparameter values according to the current invention.

FIG. 8 is a flow chart illustrating steps involved in one exemplaryprocess of substantially reducing noise and or streaks in measured databefore reconstructing CT images according to the current invention.

FIGS. 9A, 9B and 9C are shoulder images illustrating clinicallymeaningful improvement as a result of the adaptive Gaussian filterapplication according to the current invention.

FIGS. 10A, 10B and 10C are other shoulder images illustrating clinicallymeaningful improvement as a result of the adaptive Gaussian filterapplication according to the current invention.

FIGS. 11A, 11B and 11C are images of zoomed reconstructions based uponthe same data of FIGS. 10A, 10B and 10C, but they are viewed at the lungwindow.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

Referring now to the drawings, wherein like reference numerals designatecorresponding structures throughout the views, and referring inparticular to FIG. 1, a diagram illustrates one embodiment of themulti-slice X-ray CT apparatus or scanner according to the currentinvention including a gantry 100 and other devices or units. The gantry100 is illustrated from a front view and further includes an X-ray tube101, an annular frame 102 and a multi-row or two-dimensional array typeX-ray detector 103. The X-ray tube 101 and X-ray detector 103 arediametrically mounted across a subject S on the annular frame 102, whichrotates around axis RA. A rotating unit 107 rotates the frame 102 at ahigh speed such as 0.4 sec/rotation while the subject S is being movedalong the axis RA into or out of the illustrated page.

The multi-slice X-ray CT apparatus further includes a current regulator113 and a high voltage generator 109 that applies a tube voltage to theX-ray tube 101 so that the X-ray tube 101 generates X ray. In oneembodiment, the high voltage generator 109 is mounted on the frame 102.The X rays are emitted towards the subject S, whose cross sectional areais represented by a circle. The X-ray detector 103 is located at anopposite side from the X-ray tube 101 across the subject S for detectingthe emitted X rays that have transmitted through the subject S.

Still referring to FIG. 1, the X-ray CT apparatus or scanner furtherincludes other devices for processing the detected signals from X-raydetector 103. A data acquisition circuit or a Data Acquisition System(DAS) 104 converts a signal output from the X-ray detector 103 for eachchannel into a voltage signal, amplifies it, and further converts itinto a digital signal. The X-ray detector 103 and the DAS 104 areconfigured to handle a predetermined total number of projections perrotation (TPPR).

The above described data is sent to a preprocessing device 106, which ishoused in a console outside the gantry 100 through a non-contact datatransmitter 105. The preprocessing device 106 performs certaincorrections such as sensitivity correction on the raw data. A storagedevice 112 then stores the resultant data that is also called projectiondata at a stage immediately before reconstruction processing. Thestorage device 112 is connected to a system controller 110 through adata/control bus, together with a reconstruction device 114, a displaydevice 116, an input device 115, and a scan plan support apparatus 200.The scan plan support apparatus 200 includes a function for supportingan imaging technician to develop a scan plan.

One embodiment of the current invention further includes varioussoftware modules and hardware components for substantially reducingstreak and or noise in computer tomography images using a predeterminedfilter. According to one aspect of the current invention, a noisereduction device 117 of the CT apparatus advantageously performs thenoise and or streak reduction. In one embodiment, the noise reductiondevice 117 is operationally connected to other software modules and orsystem components such as the storage device 112, the reconstructiondevice 114, the display device 116 and the input device 115 via adata/control bus. In this regard, the noise reduction device 117 alonedoes not necessarily perform noise reduction functions and or theirassociated tasks in other embodiments according to the currentinvention. Furthermore, the noise reduction device 117 is optionally apart of other devices such as the reconstruction device 114 inalternative embodiments according to the current invention.

In general, projection data in CT is available after a predeterminedlog-conversion process. The log-conversion process converts measuredX-ray intensity signals that have been attenuated by a scanned objectinto line integral data. Subsequently, CT images are reconstructed fromthe line integral data by known methods of mathematical inversion. Inone exemplary embodiment of the noise/streak reduction system accordingto the current invention, the noise reduction device 117 converts theprojection data back into original x-ray intensity data or photon countmeasurements. In this case, the noise reduction device 117 needs someinformation on the system calibration process in the conversion step.Alternatively, the noise reduction device 117 has a direct access to themeasured X-ray intensity signals.

The noise reduction device 117 determines noise variance (V) of theafter-log data based upon the X-ray intensity signals or photon counts.The noise variance is computed such that the noise will be equalizedafter the log-conversion process.

To understand the effect of logarithmic conversion on the measured data,the noise model is examined with respect to variance before and afterthe log conversion. Before-log noise variance Var_(BL) is estimated by abefore-log noise model as defined in Equation (1):Var _(BL) =V _(e) +WI  (1)where Var_(BL) is the total before-log noise variance, V_(e) is theelectronic noise variance, and I is the mean count. W is the detectorgain that is function of channels, segments, a data acquisition system(DAS) and or collimation. On the other hand, after-log noise varianceVar_(AL) is estimated by an after-log noise model as defined in Equation(2):

$\begin{matrix}{\;{{Var}_{AL} = \frac{{Var}_{BL}}{I^{2}}}} & (2)\end{matrix}$Both of the above equations are disclosed in “Adaptive streak artifactreduction in CT resulting from excessive x-ray photon noise”, JiangHsieh (GE), Med. Phys. 25 (11), 2139-47, 1998.

After the noise variance has been determined, an adaptive GaussianFilterer is applied to the x-ray intensity data. One exemplary form ofthe adaptive Gaussian filter (G) is defined by Equation (3):

$\begin{matrix}{G_{\sigma} = {\frac{1}{\sqrt{2\pi\;\sigma_{G}}}{\exp\left( {- \frac{x^{2}}{2\sigma_{G}^{2}}} \right)}}} & (3)\end{matrix}$where the standard deviation (SD) σ_(G) determines the effective filterkernel size, and x is the distance between an arbitrary position and thecenter position in the kernel. A key to the successful application of anadaptive Gaussian filtering is to determine a value of the noise SDσ_(G) as a function of the local characteristics of the data or thenoise. In the embodiments of the noise and or streak reduction deviceaccording to the current invention, the variance V_(G) (or σ_(G) ²) ofthe filter kernel is adaptively determined as a function ƒ of the noisevariance Var_(AL) as defined in Equation (4):V _(G)=ƒ(Var _(AL))  (4)

The above general equation will be further explained with respect to aparticular implementation of the noise and or streak reduction deviceaccording to the current invention. Although one exemplary function inEquation (4) is defined in the following in Equation (5), this exampleis not limiting other implementations according to the currentinvention.V _(G) =K(Var _(AL))^(P)  (5)where K is a parameter for controlling filtering strength. In oneembodiment, K is set to 1. In other embodiments, the parameter K dependson a type of application, and the parameter K value is optionally ordersof magnitude. Furthermore, another parameter P is the power or exponentparameter whose typical range encompasses between 0 and 2. In oneembodiment, the exponent P value is 0.5. Other P values such as P=1 arealso optionally utilized in other embodiments for suitable applications.

FIG. 2 illustrates a relation between photon counts and measuredvariance with respect to the after-log noise model of Equation (2). Theafter-log noise model as indicated by the line closely describes trueafter-log variance values for counts 44 and higher (note that Ve˜30-40).On the other hand, as illustrated in FIG. 3, when counts become lowbelow 44 (i.e., falling onto the electronic noise floor), the measuredvariance becomes highly non-linear with respect to the after-log noisemodel. That is, the after-log noise model is not accurate for the lowcounts. Since the variance becomes huge at low counts, it is necessaryto reduce variance at low counts if the after-log data is to be used forthe noise variance determination. The variance is shown in relativevariance values as expressed in decibel (dB) based upon an arbitraryselected large value.

In embodiments of the noise and or streak reduction device according tothe current invention, the noise variance is estimated based uponprojection data after the log-conversion, and a filter is constructedbased upon the after-log variance. Subsequently, the above describedfilter is applied to the measured data or X-ray intensity data beforethe log-conversion. Lastly, the above described filtered x-ray intensitydata are converted back to projection data (i.e., line integral) domainbefore CT images are reconstructed according to the current invention.For this reason, the following exemplary filter construction method isillustrated using a Gaussian filter.

In the first filter construction method, suppose that noise at count I₀is acceptable, the desired variance level Var₀ is defined by Equation(6):Var ₀=(Ve ₀ +W ₀ I ₀)/I ₀ ²  (6)where Ve₀ and W₀ are respectively a mean value of the electronic noisevariance and the detector gain.

Furthermore, variance is reduced by low-pass filtering. That is,variance after log Var_(AL) is reduced by a certain ratio VRR to afiltered variance Var_(F) as defined in Equation (7)Var _(F) =Var _(AL) VRR  (7)where a desired reduction ratio VRR is determined by Equation (8) whenthe filtered variance Var_(F) is equal to or smaller than the desiredvariance level Var₀(Var_(F)≦Var₀):VRR=Var ₀ /Var _(AL) =Var ₀ I ² /Var _(BL)  (8)where Var_(BL) is the total before-log noise variance while Var_(AL) isthe total after-log noise variance, and I is the mean count.

Suppose the above low-pass filter is given by a predetermined set ofcoefficients {c_(K)}, where k=1 . . . N, c_(k)>0, and Σ_(k)c_(k)=1. Withrespect to the above described coefficients, the desired reduction ratioVRR is defined by Equation (9):VRR=Σ _(k) c _(k) ²  (9)

Furthermore, the coefficients {c_(k)} are optionally a N-dimensionalGaussian filter with its filter variance V_(G) as defined by Equation(10):Σ_(k) c _(k) ²=1/(4πV _(G))^(N/2)  (10)From Equations (8) through (10), the variance of the Gaussian filterV_(G) is estimated by Equations (11A) and (11B) for a dimension N.1/(4πV _(G))^(N/2) =Var ₀ I ² /Var _(BL)  (11A)V _(G)=1/(4π)(Var _(BL)(Var ₀Mean²)^(2/N)  (11B)Based upon Equation (11B), the variance of the Gaussian filter V_(G) issimplified as expressed in Equation (11C) with two variables VarScaleand VarPower. In fact, Equation (11c) is tantamount to Equation (5),where the parameters K and P of Equation (5) respectively correspond toVarScale and VarPower of Equation (11C). In the current application, theparameters K and P of Equation (5) and VarScale and VarPower of Equation(11C) are interchangeable. According to the first filter constructionmethod, Equation (11C) defines the variance of the Gaussian filterV_(G):V _(G) =VarScale Var _(AL) ^(VarPower)  (11C)Where Var_(AL) is already defined by Equation (2). Finally, the varianceof the Gauss filter V_(G) is determined from the after-log noisevariance Var_(AL) with the two variables VarScale and VarPower. Thevariable VarScale is also defined by Equation (12) with respect to thepreviously defined Var₀ from Equation (6). According to the first filterconstruction method, Equation (12) defines the variable VarScale:VarScale=1/(4π)(1/Var ₀)^(2/N)  (12)On the other hand, the other variable VarPower is defined in Equation(13), and the value is easily determined for 2D, 3D and 4D filters inembodiments of the noise and or streak reduction device according to thecurrent invention. According to the first filter construction method,Equation (13) defines the variable VarPower:

$\begin{matrix}\begin{matrix}{{VarPower} = {2/N}} \\{= {1\mspace{14mu}{for}\mspace{14mu} 2D\mspace{14mu}{Gaussian}\mspace{14mu}{filters}}} \\{= {2/3}} \\{= {0.67\mspace{14mu}{for}\mspace{14mu} 3D\mspace{14mu}{Gaussian}\mspace{14mu}{filters}}} \\{= {{1/2}\mspace{14mu}{for}\mspace{14mu} 4D\mspace{14mu}{Gaussian}\mspace{14mu}{filters}}}\end{matrix} & (13)\end{matrix}$

Now referring to FIG. 4, a graph illustrates a relationship between theeffective filter size of the Gauss filter and the count with respect tothe dimension N, VarScale and VarPower using a predetermined Gaussianfilter. With a particular value of the dimension N, ranging from 1through 4, the VarPower value ranges from 2 to 0.5. On the other hand,the VarScale values have a wider range from 406.00-75 to 0.6726. Asshown, at N=4, the variance is constant over the widest range of thecounts. On the other hand, at N=1, the variance is constant over thenarrowest range of the counts. The ranges of VarPower and VarScale arenot limited to the above disclosed value ranges in other embodiments inorder to practice the current invention. In fact, VarPower optionallyranges from 1 to 10000 while VarPower optionally ranges from 0.2 to 1according to certain other aspects of the invention.

As described above, in embodiments of the noise and or streak reductiondevice according to the current invention, the noise variance isestimated based upon projection data after the log-conversion, and afilter is constructed based upon the after-log variance. Subsequently,the above described filter is applied to the measured data or X-rayintensity data before the log-conversion. Lastly, the above describedfiltered x-ray intensity data are converted back to projection data(i.e., line integral) domain before CT images are reconstructedaccording to the current invention. As a result of the above describedfilter application, the log converted projection data has substantiallyuniform variance.

In general, total variance in measured data depends upon both Poissonianand Gaussian noise. Although the count data from detector is ideally ofPoissonian distribution, the actual data is compounded with Gaussiandistributed electronic noise that is induced in the data acquisitionsystem (DAS) circuitry. In reconstructed images, since the low countdata produces the streaks and intolerable noise, electronic noise is nolonger negligible at low counts. Thus, an accurate noise model shouldtake both Poissonian and Gaussian noise into account.

Equations (11A), (11B) and (11C) assume infinite Gaussian kernel. Inpractice, the Gaussian kernel is limited to a definite mask such as 5×7.For further implementation of the noise and or streak reduction devicesuch as the noise reduction device 117, Equation (14) defines one way todetermine discrete Gaussian filtering for each of the measured datavalues. That is, the discrete kernel of the filter for a particulardetector element (i) is defined by:

$\begin{matrix}{I_{i_{0}}^{G} = \frac{\sum\limits_{i}{I_{i}{\exp\left( {- \frac{\Delta\; x_{i}^{2}}{2V_{i_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0}} - I_{i}} \right)^{2}}{2V_{R}}} \right)}}}{\sum\limits_{i}{{\exp\left( {- \frac{\Delta\; x_{i}^{2}}{2V_{i_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0}} - I_{i}} \right)^{2}}{2V_{R}}} \right)}}}} & (14)\end{matrix}$where Δr_(i) is the distance of a i^(th) pixel in a one dimensional (1D)detector to a predetermined reference pixel i₀ and Vi₀ is the frequencyresponse of the filter at the reference pixel i₀. V_(R) is a parameterof the filter.

By the same token, the noise reduction device 117 determines discreteGaussian filtering for each of the measured data values in a twodimensional (2D) detector. That is, the discrete kernel of the filterfor a particular detector element (i,j) is defined by Equation (15):

$\begin{matrix}{I_{({i_{0},j_{0}})}^{G} = \frac{\sum\limits_{i,j}{I_{i,j}{\exp\left( {- \frac{\Delta\; x_{i,j}^{2}}{2V_{i_{0},j_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0},j_{0}} - I_{i,j}} \right)^{2}}{2V_{R}}} \right)}}}{\sum\limits_{i,j}{{\exp\left( {- \frac{\Delta\; x_{i,j}^{2}}{2V_{i_{0},j_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0},j_{0}} - I_{i,j}} \right)^{2}}{2V_{R}}} \right)}}}} & (15)\end{matrix}$where Δr_(i,j) is the distance of a (i^(th), j^(th)) pixel in a 2Ddetector to a predetermined reference pixel (i₀, j₀) and Vi₀, j₀ is thefrequency response of the filter at the reference pixel (i₀, j₀). V_(R)is a parameter of the filter.

Contrary to prior art attempts, the embodiments of the noise and orstreak reduction device according to the current invention estimate thenoise variance based upon the noise characteristics of projection dataafter the log-conversion, and a filter is constructed based upon theafter-log estimated variance. Subsequently, the above described filteris applied to the original measured data or X-ray intensity data beforethe log-conversion. Lastly, the above described filtered x-ray intensitydata are converted back to projection data (i.e., line integral) domainbefore CT images are reconstructed according to the current invention.

In certain embodiments, the above described steps of substantiallyminimizing the noise and or streak are optionally iterated for severaltimes to achieve a desirable noise reduction effect. In theseembodiments, the parameters p and K optionally vary for desiredsolutions. Furthermore, the parameters p and K optionally vary for eachinstance of iteration.

To determine clinically useful values of the parameters K and P ofEquation (5) or VarScale and VarPower of Equation (11C) in the abovedescribed noise and or streak reduction process, an optimal noise filteris constructed as iterative reconstruction (IR) noise model filtering.In general, the role of pure raw data filtering is to remove the effectof electronic noise or photon starvation. Logarithmic conversion resultsin unreliable raw data at low values, so lower statistical weight areassigned to these data. Thus, the pure raw data filtering and thestatistical weight complement each other. For these reasons, theembodiments of the noise and or streak reduction device according to thecurrent invention do not require strong data filtering such as imageregularization based upon total variation (TV) or Adaptive WeightedAnisotropic Diffusion (AWAD). In summary, the IR noise model filteringimproves to preserve the spatial resolution for low dose data by usingweak filtering parameters.

Other variations in the parameters are illustrated in the followingexamples. Now referring to FIG. 5, a graph illustrates a relationbetween the mean count and the after-log variance in an embodiment ofthe noise and or streak reduction device using a predetermined filteraccording to the current invention. Assuming infinite Gaussian kernel,the parameter K of Equation (5) or VarScale of Equation (11C) has beenadjusted at 1, 10 and 100 while the parameters P of Equation (5) orVarPower of Equation (11C) is fixed at 1. Without any filter, thereappears to be no noise-equalizing in the after-log variance across themean count. At k=1, there appears to be some noise-equalizing effect inthe after-log variance in a small low mean count region below 30. Atk=10, there appears to be significant noise-equalizing effect in theafter-log variance over a wide mean count region below 160. Lastly,k=100, there appears to be noise-significant equalizing effect in theafter-log variance over all mean count regions below 200. The varianceis shown in relative variance values as expressed in decibel (dB) basedupon an arbitrary selected large value.

Now referring to FIG. 6, a graph illustrates a relation between the meancount and the after-log variance in an embodiment of the noise and orstreak reduction device using a predetermined filter according to thecurrent invention. Assuming infinite Gaussian kernel, the parameter theparameters P of Equation (5) or VarPower of Equation (11C) has beenadjusted at 1, 0.75 and 0.5 while the parameter K of Equation (5) orVarScale of Equation (11C) is fixed at 1. Without any filter, thereappears to be no noise-equalizing in the after-log variance across themean count. At P=1, there appears to be some noise-equalizing effect inthe after-log variance in a small low mean count region below 30. AtP=0.75, although there appears to be also some noise-equalizing effectin the after-log variance over a slightly wider mean count region below50, the equalizing effect is not achieving a completely flat equalizedregion. Lastly, P=0.5, there appears to be significant noise-equalizingeffect in the after-log variance over substantially wider mean countregions below 200. The noise-equalizing effect appears to be significantbetween the mean count between 60 and 200: The variance is shown inrelative variance values as expressed in decibel (dB) based upon anarbitrary selected large value.

Now referring to FIG. 7, a graph illustrates a relation between the meancount and the after-log variance in an embodiment of the noise and orstreak reduction device using a predetermined filter according to thecurrent invention. Assuming infinite Gaussian kernel, the parameter K ofEquation (5) or VarScale of Equation (11C) has been adjusted at 1, 1.5and 2 while the parameters P of Equation (4) or VarPower of Equation(11C) is fixed at 0.5. Without any filter, there appears to be nonoise-equalizing in the after-log variance across the mean count. AtK=1, there appears to be some noise-equalizing effect in the after-logvariance in a small low mean count region below 180. At K=1.5, thereappears to be some noise-equalizing effect in the after-log varianceover a slightly wider mean count region below 380. Lastly, K=2.0, thereappears to be noise-equalizing effect in the after-log variance over awider count region below 800. The variance is shown in relative variancevalues as expressed in decibel (dB) based upon an arbitrary selectedlarge value.

Now referring to FIG. 8, a flow chart illustrates steps involved in oneexemplary process of substantially reducing noise and or streaks inmeasured data before reconstructing CT images according to the currentinvention. In general, projection data in CT is available after apredetermined log-conversion process. The log-conversion processconverts measured X-ray intensity signals that have been attenuated by ascanned object into line integral data. Subsequently, CT images arereconstructed from the line integral data by known methods ofmathematical inversion.

In one exemplary embodiment of the noise/streak reduction processaccording to the current invention, the following steps are performed bya predetermined combination of software and hardware. Implementation ofthe process is not limited to any particular software or hardwaremodules.

The noise reduction process determines noise variance (V) of themeasurement data based upon the X-ray intensity signals or photon countsin a step S20. The noise variance s computed such that the noise will beequalized after the log-conversion process. The after-log noise varianceVar_(AL) is determined by the noise model as defined in above Equation(2), which takes the measured x-ray intensity or photon count I and theelectronic noise Ve such as a data acquisition system into account basedupon Equation (1).

After the after-log noise variance Var_(AL), has been determined in thestep S20, an adaptive Gaussian Filterer is applied in a step S30 to thex-ray intensity data from the step S10. One exemplary form of theadaptive Gaussian filter (G) is defined by above Equation (3). Theadaptive Gaussian filter relies on the standard deviation a to determinethe effective filter kernel size and the distance x between an arbitraryposition and the center position in the kernel. An adaptive Gaussianfiltering is successfully applied to a value of the noise SD σ as afunction of the local characteristics of the data or the noise. In theexemplary process of substantially reducing noise and or streaksaccording to the current invention, the variance V_(G) (or σ_(G) ²) ofthe filter kernel is adaptively determined as a function ƒ of the noisevariance V as defined in above Equation (4). A particular implementationof the noise and or streak reduction process involves a parameter K forcontrolling filtering strength. In one embodiment, K is set to 1. Inother embodiments, the parameter K depends on a type of application, andthe parameter K value is optionally orders of magnitude. Furthermore,the particular implementation of the noise and or streak reductionprocess also involves a second parameter P, which is the power orexponent parameter whose typical range encompasses between 0 and 2. Inone process, the exponent P value is 0.5. Other p values such as P=1 arealso optionally utilized in other processes for suitable applications.The above described parameters K and P are respectively interchangeablewith VarScale and VarPower of above Equation (11c) in the exemplaryprocess of substantially reducing noise and streaks according to thecurrent invention.

In further implementation detail of the step S30, one way to determinediscrete Gaussian filtering for each of the measured data values isdefined for a particular one dimensional (1D) detector element (i) byabove Equation (14). Similarly, one way to determine discrete Gaussianfiltering for each of the measured data values is defined for aparticular two dimensional (2D) detector element (i, j) by aboveEquation (15). The discrete Gaussian filter kernel is constructed andapplied to each of the measured data within the step S30. Contrary toprior art attempts, the above described exemplary process ofsubstantially reducing the noise and or streaks according to the currentinvention estimates the noise variance based upon the noisecharacteristics of projection data after the log-conversion, and afilter is constructed based upon the after-log estimated variance in thesteps S20. Subsequently, the above described filter is applied in thestep S30 to the original measured data or X-ray intensity data beforethe log-conversion.

Optionally, the steps S20 and S30 are iteratively repeated in certainapplications in the exemplary process according to the currentinvention. To be optionally iterated, a step S40 determines whether ornot that the exemplary process proceeds back to the step S20. If thestep S40 determines that the filter is to be iteratively applied, theexemplary process repeats from the step S20. On the other hand, if thestep S40 determines that the filter is not iteratively applied or theiteration has completed, the exemplary process goes a step S50. Lastly,in the step S50, the above described filtered x-ray intensity data areconverted back to projection data (i.e., line integral) domain before CTimages are reconstructed according to the current invention.

Now referring to FIGS. 9A, 9B and 9C, shoulder images illustrateclinically meaningful improvement as a result of the adaptive Gaussianfilter application according to the current invention. The variance ofDAS electronic noise, Ve is determined from real scan data which wasacquired without turning the X-ray tube. The only filter parameter is K,which was set to 1 in all testing cases of FIGS. 9A, 9B and 9C.Furthermore, the images as shown in FIGS. 9A, 9B and 9C were acquiredwith 160-row detector at 120 kv and 195 mAs with +69.5 mm/rotation couchspeed. FIG. 9A shows the reconstructed image without data domainfiltering by the adaptive Gaussian filter according to the currentinvention. FIG. 9B shows the reconstructed image with data domainfiltering by the adaptive Gaussian filter according to the currentinvention. FIG. 9B shows that the streaks and noise have beensubstantially suppressed by the adaptive Gaussian filter according tothe current invention. In other words, the streaks and noise haveobstructed and or obscured clinically relevant information in FIG. 9A.On the other hand, FIG. 9B delineates the above clinically relevantinformation. Lastly, FIG. 9C illustrates the difference image that showsalmost no loss of structural information.

Now referring to FIGS. 10A, 10B and 10C, other shoulder imagesillustrate clinically meaningful improvement as a result of the adaptiveGaussian filter application according to the current invention. Theimproved quality is almost consistent in all cases. The variance of DASelectronic noise, Ve is determined from real scan data which wasacquired without turning the X-ray tube. The only filter parameter is K,which was set to 1 in all testing cases of 10A, 10B and 10C.Furthermore, the images were acquired with 64-row detector at 120 kv and30 mAs with +47.5 mm/rotation couch speed. FIG. 10A shows thereconstructed image without data domain filtering by the adaptiveGaussian filter according to the current invention. FIG. 10B shows thereconstructed image with data domain filtering by the adaptive Gaussianfilter according to the current invention. FIG. 10B shows that thestreaks and noise have been substantially suppressed by the adaptiveGaussian filter according to the current invention. In other words, thestreaks and noise have obstructed and or obscured clinically relevantinformation in FIG. 10A. On the other hand, FIG. 10B delineates theabove clinically relevant information. Lastly, FIG. 10C illustrates thedifference image that shows almost no loss of structural information.

Now referring to FIGS. 11A, 11B and 11C, images are zoomedreconstructions based upon the same data of FIGS. 10A, 10B and 10C, butthey are viewed at the lung window. As clearly seen, the streaks havebeen substantially removed in FIG. 11B without apparent resolutiondegradation in the lung tissue. Although a cloud-like smear is clearlyobserved in a lower lung region in FIG. 11B, it is ambiguous in FIG.11A. Some blooming effect is observed in the ribs. This may be caused bythe extremely low observing window level (−700 HU), which is at thebottom of the bone intensity elevation. There is no apparent structuralinformation in the difference image FIG. 11B except for a dark hint ofthe vessel in a area that is slightly above the center.

It is to be understood, however, that even though numerouscharacteristics and advantages of the present invention have been setforth in the foregoing description, together with details of thestructure and function of the invention, the disclosure is illustrativeonly, and that although changes may be made in detail, especially inmatters of shape, size and arrangement of parts, as well asimplementation in software, hardware, or a combination of both, thechanges are within the principles of the invention to the full extentindicated by the broad general meaning of the terms in which theappended claims are expressed.

What is claimed is:
 1. A method of equally reducing noise in measuredsignals, comprising the steps of: a) determining a relative value innoise variance at each of the measured signals based upon a function ofa predetermined noise model to generate a noise-model based variance; b)automatically generating a discrete filter kernel of a noise-equalizingfilter for each of the measured signals based upon the noise-model basedvariance; and c) applying the discrete filter kernel to a correspondingone of the measured signals to generate a filtered measured signals. 2.The method of processing measured signals according to claim 1 whereinthe noise-model based variance is defined by the measured signal and aknown electronic noise value.
 3. The method of processing measuredsignals according to claim 2 wherein the noise-model based variance is$\frac{1 + {V_{e}/I}}{I},$ where the I is the measured signal whileV_(e) is the known electronic noise value.
 4. The method of processingmeasured signals according to claim 3 wherein the discrete kernel of thefilter for a particular detector element (i) is defined by$I_{i_{0}}^{G} = \frac{\sum\limits_{i}{I_{i}{\exp\left( {- \frac{\Delta\; x_{i}^{2}}{2V_{i_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0}} - I_{i}} \right)^{2}}{2V_{R}}} \right)}}}{\sum\limits_{i}{{\exp\left( {- \frac{\Delta\; x_{i}^{2}}{2V_{i_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0}} - I_{i}} \right)^{2}}{2V_{R}}} \right)}}}$where Δx_(i) is the distance of a i^(th) pixel in 1D to a predeterminedreference pixel i₀ and Vi₀ is the frequency response of the filter atthe reference pixel i₀, V_(R) is a parameter of the filter.
 5. Themethod of processing measured signals according to claim 3 wherein thediscrete kernel of the filter for a particular detector element (i, j)is defined by$I_{({i_{0},j_{0}})}^{G} = \frac{\sum\limits_{i,j}{I_{i,j}{\exp\left( {- \frac{\Delta\; x_{i,j}^{2}}{2V_{i_{0},j_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0},j_{0}} - I_{i,j}} \right)^{2}}{2V_{R}}} \right)}}}{\sum\limits_{i,j}{{\exp\left( {- \frac{\Delta\; x_{i,j}^{2}}{2V_{i_{0},j_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0},j_{0}} - I_{i,j}} \right)^{2}}{2V_{R}}} \right)}}}$where Δx_(i,j) is the distance of a (i^(th), j^(th)) pixel in 2D to apredetermined reference pixel (i₀, j₀) and Vi₀, j₀ is the frequencyresponse of the filter at the reference pixel (i₀, j₀), V_(R) is aparameter of the filter.
 6. The method of processing measured signalsaccording to claim 2 further comprising an additional step of iteratingsaid steps a), b) and c).
 7. The method of processing measured signalsaccording to claim 2 wherein the noise-equalizing filter is a high passfilter including a Gaussian filter.
 8. A system for equally reducingnoise in measured signals, comprising: a noise reduction device forperforming the tasks of determining a noise variance at each of themeasured signals based upon a function of a predetermined noise model togenerate a noise-model based variance, said noise reduction deviceperforming the tasks of automatically generating a discrete filterkernel of a noise-equalizing filter for each of the measured signalsbased upon the noise-model based variance, said noise reduction deviceperforming the tasks of applying the discrete filter kernel to acorresponding one of the measured signals to generate a filteredmeasured signal.
 9. The system for processing measured signals accordingto claim 8 wherein the noise-model based variance is defined by themeasured signal and a known electronic noise value.
 10. The system forprocessing measured signals according to claim 9wherein the noise-modelbased variance is $\frac{1 + {V_{e}/I}}{I},$ where the I is the measuredsignal while V_(e) is the known electronic noise value.
 11. The systemfor processing measured signals according to claim 10 wherein thediscrete kernel of the filter for a particular detector element (i) isdefined by$I_{i_{0}}^{G} = \frac{\sum\limits_{i}{I_{i}{\exp\left( {- \frac{\Delta\; x_{i}^{2}}{2V_{i_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0}} - I_{i}} \right)^{2}}{2V_{R}}} \right)}}}{\sum\limits_{i}{{\exp\left( {- \frac{\Delta\; x_{i}^{2}}{2V_{i_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0}} - I_{i}} \right)^{2}}{2V_{R}}} \right)}}}$where Δx_(i) is the distance of a i^(th) pixel in 1D to a predeterminedreference pixel i₀ and Vi₀ is the frequency response of the filter atthe reference pixel i₀, V_(R) is a parameter of the filter.
 12. Thesystem for processing measured signals according to claim 10 wherein thediscrete kernel of the filter for a particular detector element (i, j)is defined by$I_{({i_{0},j_{0}})}^{G} = \frac{\sum\limits_{i,j}{I_{i,j}{\exp\left( {- \frac{\Delta\; x_{i,j}^{2}}{2V_{i_{0},j_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0},j_{0}} - I_{i,j}} \right)^{2}}{2V_{R}}} \right)}}}{\sum\limits_{i,j}{{\exp\left( {- \frac{\Delta\; x_{i,j}^{2}}{2V_{i_{0},j_{0}}}} \right)}{\exp\left( {- \frac{\left( {I_{i_{0},j_{0}} - I_{i,j}} \right)^{2}}{2V_{R}}} \right)}}}$where Δx_(i,j) is the distance of a (i^(th), j^(th)) pixel in 2D to apredetermined reference pixel (i₀, j₀) and Vi₀, j₀ is the frequencyresponse of the filter at the reference pixel (i₀, j_(o)),V_(R xis a parameter of the filter.)
 13. The system for processingmeasured signals according to claim 9 wherein said noise reductiondevice iterates each of the tasks.
 14. The system for processingmeasured signals according to claim 9 wherein the noise-equalizingfilter is a high pass filter including a Gaussian filter.
 15. A methodof equally reducing noise in measured signals, comprising the steps of:a) determining a noise variance at each of the measured signals basedupon a function of a predetermined noise model; b) automaticallygenerating a discrete filter kernel of a noise-equalizing filter foreach of the measured signals based upon the noise variance; and c)applying the discrete filter kernel to a corresponding one of themeasured signals to generate a filtered measured signals, wherein thenoise variance is $\frac{1 + {V_{e}/I}}{I},$ where the I is the measuredsignal while V_(e) is a known electronic noise value.
 16. A system forequally reducing noise in measured signals, comprising: a noisereduction device for performing the tasks of determining a noisevariance at each of the measured signals based upon a function of apredetermined noise model, said noise reduction device performing thetasks of automatically generating a discrete filter kernel of anoise-equalizing filter for each of the measured signals based upon thenoise variance, said noise reduction device performing the tasks ofapplying the discrete filter kernel to a corresponding one of themeasured signals to generate a filtered measured signal, wherein thenoise variance is $\frac{1 + {V_{e}/I}}{I},$ where the I is the measuredsignal while Ve is a known electronic noise value.